qttools.greens_function_solver.inv#

Classes

source class Inv(max_batch_size: int = 100)

Selected inversion solver based on dense matrix inversion.

Warning

This solver will densify the matrix to invert it. It is intended as a reference implementation and should not be used in production code.

Initializes the selected inversion solver.

Parameters

max_batch_size : int, optional — Maximum batch size to use when inverting the matrix, by default 100.

Methods

source method Inv.selected_inv(a: DSDBSparse, obc_blocks: OBCBlocks | None = None, out: DSDBSparse | None = None) → None | DSDBSparse

Performs selected inversion of a block-tridiagonal matrix.

This method will densify the matrix, invert it, and then select the elements to keep by matching the sparse structure of the input matrix.

Parameters

a : DSDBSparse — Matrix to invert.
obc_blocks : OBCBlocks, optional — OBC blocks for lesser, greater and retarded Green's functions. By default None.
out : DSDBSparse, optional — Preallocated output matrix, by default None.

Returns

None | DSDBSparse — If out is None, returns None. Otherwise, returns the inverted matrix as a DSDBSparse object.

source method Inv.selected_solve(a: DSDBSparse, sigma_lesser: DSDBSparse, sigma_greater: DSDBSparse, obc_blocks: OBCBlocks | None = None, out: tuple[DSDBSparse, ...] | None = None, return_retarded: bool = False, return_current: bool = False) → None | tuple

Produces elements of the solution to the congruence equation.

This method produces selected elements of the solution to the relation:

\[ X^{\lessgtr} = A^{-1} \Sigma^{\lessgtr} A^{-\dagger} \]

Parameters

a : DSDBSparse — Matrix to invert.
sigma_lesser : DSDBSparse — Lesser matrix. This matrix is expected to be skew-hermitian, i.e. \(\Sigma_{ij} = -\Sigma_{ji}^*\).
sigma_greater : DSDBSparse — Greater matrix. This matrix is expected to be skew-hermitian, i.e. \(\Sigma_{ij} = -\Sigma_{ji}^*\).
obc_blocks : OBCBlocks, optional — OBC blocks for lesser, greater and retarded Green's functions. By default None.
out : tuple[DSDBSparse, ...] | None, optional — Preallocated output matrices, by default None
return_retarded : bool, optional — Wether the retarded Green's function should be returned along with lesser and greater, by default False
return_current : bool, optional — Whether to compute and return the current for each layer via the Meir-Wingreen formula. By default False. This option is not implemented.

Returns

None | tuple — If out is None, returns None. Otherwise, the solutions are returned as DSBParse matrices. If return_retarded is True, returns a tuple with the retarded Green's function as the last element.

Raises